The horrific discovery Monday of the bodies of three kidnapped Israeli teenagers — one of them a US citizen — should destroy the myth of a new, moderate Hamas.

All Israel was plunged into mourning upon learning that Naftali Frenkel, 16, Gilad Shaar, 16, and Eyal Yifrach, 19, had been found shot and bound, their bodies hastily buried in a field.

Frenkel was the grandson of American immigrants; many of his relatives still live in Brooklyn. The three apparently were killed almost immediately after they were seized 19 days ago.

This is cold-blooded murder. But it has a perverse logic, for its popularity on the Palestinian street will translate into support for Hamas against Palestinian President Mahmoud Abbas — whose so-called support for Israel’s search was almost entirely rhetorical.

As for Prime Minister Benjamin Netanyahu, he rightly regards the killings as a war crime, and his priority now is to demonstrate to Hamas that Israel will do whatever it takes to protect its citizens.

At the least, we would expect the Obama administration to end America’s political and financial support for the “unity” government under which Abbas recently joined forces with Hamas.

Meanwhile, even as President Obama has condemned the murders, he lumped Israel along with Hamas in a warning against “steps that could further destabilize the situation.”

Surely President Obama and Secretary of State John Kerry should instead be asking themselves what they think will be accomplished by lending American dollars to those who murder teens — and pressing Israel to talk peace with them.